Suppose now the economy is described by a New Keynesian Model, where weassume rational expectations. The equilibrium is described by the following threeequations, in order the Dynamic IS, the New Keynesian PC and the MonetaryPolicy Rule:1Y₁ = E₁Y₁+1 = = rt+u!S;Yt Etyt+1(1)T4+ = BETCH+1+ky tuổi(2)rt = Y¬πt + YyYt + UMP(3)where u¹S, u and uISMP are white noise, iid disturbances identifying output, infla-tion and interest rate shocks, respectively. Then, 0, ß, к are positive model's (con-volution of) structural parameters and 4 and yy are positive policy parameters.Because of the absence of any backward-looking elements and any informationabout the future values of the disturbances, Ett+1 = Etyt+1 = 0. Find a solution for πt, уt and r₁ as function of the disturbances and the pa-rameters of the model. What are the effects of an unfavorable inflation shock(i.e. uŢ increases) on output, interest rate and inflation in this case? Interpretyour answer.

The policy undertaken by the central bank of a nation to stabilize the economy is referred to as a…

Find a solution for πt, yt and r₺ as function of the disturbances and the pa- rameters of the model. What are the effects of an unfavorable inflation shock (i.e. u increases) on output, interest rate and inflation in this case? Interpret your answer.

Find a solution for πt, yt and r₺ as function of the disturbances and the pa- rameters of the model. What are the effects of an unfavorable inflation shock (i.e. u increases) on output, interest rate and inflation in this case? Interpret your answer.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Suppose now the economy is described by a New Keynesian Model, where we
assume rational expectations. The equilibrium is described by the following three
equations, in order the Dynamic IS, the New Keynesian PC and the Monetary
Policy Rule:
1
Y₁ = E₁Y₁+1 = = rt+u!S;
Yt Etyt+1
(1)
T4+ = BETCH+1+ky tuổi
(2)
rt = Y¬πt + YyYt + UMP
(3)
where u¹S, u and u
IS
MP are white noise, iid disturbances identifying output, infla-
tion and interest rate shocks, respectively. Then, 0, ß, к are positive model's (con-
volution of) structural parameters and 4 and yy are positive policy parameters.
Because of the absence of any backward-looking elements and any information
about the future values of the disturbances, Ett+1 = Etyt+1 = 0.

Find a solution for πt, уt and r₁ as function of the disturbances and the pa-
rameters of the model. What are the effects of an unfavorable inflation shock
(i.e. uŢ increases) on output, interest rate and inflation in this case? Interpret
your answer.

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